I think you're on the right track but I suggest looking at a smaller 3S battery, something down in the 2000mAh range. I run a 2S 1600 or a 3S 1800 and a 3S 2000 in my trucks. As long as your'e staying with low-wind motors, the amp draw isn't an issue and run-time isn't either. The benefit here is that the lower mAh packs are physically smaller, thus allowing you to mount them in different places. A 3S 5000 is a brick and takes up a lot of space. It can be done but these small packs still run 45minutes or more at times.
Tekin, Novak, Holmes Hobbies are a few well-known brands. In my opinion a 35T will give you plenty of speed on 3S. I've run a 55T on 2S before and it topped out at about 7MPH. My guess is the 35T / 3S should clip the high teens / 20mph. I run a sensored brushless system in my trucks. One has an Integy 31.5T motor w/ a SpeedPassion ESC on 2S and the other (being upgraded at the moment) is a TrakPower 21.5T sensored system powered by 3S. As stated, it's still under partial construction but I expect it to have power to crawl but can "burst" to hop out of a tight spot when needed.
If you choose to go brushless then it has to be a sensored system. Unsensored systems will cog and are unpleasant when trying to drive slow. Brushed motors don't have that issue which is why they're a popular choice.
As far as the winch issue, there are of course a few ways to do it but I suggest the BEC regardless. It will allow more current flow and you don't have to worry about accessories draining your ESCs BEC circuit which can cause a shutdown. Just set the output to what your servos can handle. Otherwise some guys will run a separate power source to the winch if they want to deliver more voltage than the servos can handle. The ESC could probably handle that servo on it's own but I still advise running it off the BEC for assurance and reliability.